Of course, a name can give a false or misleading impression too. But you get the general picture: it's part of the big, broad inner London landscape, a collage of social types and cultures with family connections all over the world. Whichever ones I'm teaching, the experience is highly educational: sweet, rewarding, sometimes saddening.

It's not a huge investment of my time: just 20 minutes with a few of them while the others are at assembly. Last term I read aloud from storybooks to groups of up to six and encouraged them to take turns reading too. Now I'm working with two at a time, playing a game called Upwords. It's like Scrabble except that the letters don't have score values and you're allowed to stack tiles on top of others that are already on the board. Hence "hat" can be transformed into "sat", "rat", "mat" and so on.

The children's competence at this task varies greatly. One day I'll be applauding "focus", "hex" or "vault" (though in the latter case I had to insert the "u"), another I'll be bending the rules to allow "ok" or "tv" because I've already had to explain that "mrb" and "spi" aren't words, and I cannot – really must not – look into that child's eyes and tell them yet again that they have failed.

Why not? Because it's in those moments that the strutting certainties of education conservatives are revealed to be hot air and the stats and prescriptions of New Labour as vacuities. It takes no dazzling powers of insight to glean – from their speech, their demeanour, their clothes – that the children who find the game hardest tend to be those from hard-up homes where books and academic learning are less likely to be prized. No special knowledge is required to detect that some are already resigning themselves to not making the educational grade, although the facts are there to prove the point: kids from poorer and non-professional backgrounds who were on a par with middle-class peers when they started at school begin to slip behind from age eight or nine and mostly keep on slipping. It is my duty to do all I credibly can to arrest that slide. If that means pragmatically accepting "tv" as a word for the time being, then so be it.

Perhaps some such children aren't very bright. Perhaps. But let me mention one in particular with whom I work. Her vocabulary is poor and her concentration wanders. She needs a lot of help and hints to construct any words at all and I heap praise on her every small success. Mostly she wants to talk about her pet dog's terrible farts and how come I've got a scab on my knuckle (a small gardening mishap, since you ask). "You could pick that off," she gravely informs me. "Can I pick it off for you?"

The other day, though, she asked about Queen Victoria. When did she die? Where did she live and who lives there now? And what about the Elephant Man? When did he die? Was I born before he died? And why is there a "p" in "elephant"? I don't claim that such questions demonstrate latent genius or even latent middle-management potential. I do, though, cite it as evidence of a bubbling curiosity that craves an outlet for expression and a receptive ear. The child has a thirst for knowledge and understanding, and even her impressive teacher cannot quench it – there is only one of him after all.

But the real question here is not about individual teachers or schools, but the core values of our education system. I'd guess that targets and tests and achievement rhetoric have little meaning for children like that girl; that they may even exclude more than they inspire. But that doesn't mean they don't love learning. Why aren't we better at nurturing that love?